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Reflecting Squarely

In how many ways can you fit all three pieces together to make shapes with line symmetry?

Eight Dominoes

Using the 8 dominoes make a square where each of the columns and rows adds up to 8

Rhombicubocts

Each of these solids is made up with 3 squares and a triangle around each vertex. Each has a total of 18 square faces and 8 faces that are equilateral triangles. How many faces, edges and vertices does each solid have?

Shady Symmetry

Age 11 to 14
Challenge Level

Charlie created a symmetrical pattern by shading in four squares on a 3 by 3 square grid:
pattern with squares

Alison created a symmetrical pattern by shading in two triangles on a 3 by 3 isometric grid:

pattern with triangles
Choose whether you would like to work on square grids or isometric grids.
 
How many different symmetrical patterns can you make?
  
Here are some questions you might like to consider:
  • How many different patterns can you make if you are only allowed to shade in one... two... three... four cells?
  • How does the number of patterns with 6 cells shaded relate to the number with 3 cells shaded?
  • Can you make patterns with exactly one... two... three... four lines of symmetry?
  • Can you make patterns with rotational symmetry AND lines of symmetry?
  • Can you make patterns with rotational symmetry but NO lines of symmetry?
  • Can you make patterns using more than one colour?
 

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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